The structure InflatonPotentialCert bundles five properties of the inflaton potential on the recognition manifold.
(1) In plain English, it certifies that V(φ_inf) := Jcost(1 + φ_inf) satisfies: vacuum energy is zero at the reference point; the potential is nonnegative for displacements φ_inf > -1; it is strictly positive away from vacuum; it obeys the same reciprocal symmetry as Jcost; and it takes the explicit quadratic form φ_inf² / (2(1 + φ_inf)).
(2) In Recognition Science this matters because the J-cost is the unique cost function forced by the framework's functional equation. Using it directly as the inflaton potential shows that slow-roll inflation emerges from the same recognition cost that governs all other physics, without additional parameters.
(3) The formal statement is a Lean structure whose five fields are theorems: vacuum : V 0 = 0, nonneg : ∀ {phi_inf}, -1 < phi_inf → 0 ≤ V phi_inf, pos_off_vacuum : ∀ {phi_inf}, phi_inf ≠ 0 → -1 < phi_inf → 0 < V phi_inf, reciprocal_symm : ∀ {phi_inf}, -1 < phi_inf → V phi_inf = V ((1 + phi_inf)⁻¹ - 1), and quadratic_form : ∀ {phi_inf}, -1 < phi_inf → V phi_inf = phi_inf ^ 2 / (2 * (1 + phi_inf)). The definition inflatonPotentialCert supplies a concrete inhabitant by plugging in the proved lemmas V_vacuum, V_nonneg, V_pos_off_vacuum, V_reciprocal_symm and V_eq_quadratic.
(4) Visible dependencies inside the supplied source are the definition V and the five supporting theorems listed above, all in the same module; they rest on Jcost properties imported from Cost but are not re-proved here.
(5) The declaration does not prove slow-roll parameters ε_V or η_V, the spectral index n_s, the tensor-to-scalar ratio r, or any dynamical evolution of the inflaton field; those claims appear only in the module's documentation as motivation.